The present invention relates to a method of detecting breaks in logging signals relating to a region of a medium, the logging signals being made up of logs of different kinds recorded for the said region as a function of depth, and the application of this method to a depthwise readjustment of the said logs.
In numerous fields, it is necessary to rapidly correlate two or more curves representing the variations of a first quantity as a function of a second quantity, for purposes of comparison, fitting, etc.
The curves to be compared may be of the same kind, that is to say represent the variations of one and the same first quantity as a function of one and the same second quantity, or of different kinds. They may for example be recordings of one and the same physical phenomenon which are however shifted in time or space, or recordings relating to different physical phenomena or else recordings relating to one and the same physical phenomenon recorded for example by different methods so that their frequency content is different.
The correlations may be performed numerically. The result obtained is generally global and rather unreliable if no constraining assumptions are made regarding the signals, the method then consisting in choosing between several autocorrelation peaks. The correlation can be performed visually, by manually shifting one of the curves with respect to the other along the axis of the second quantity. In this way, optimal similitude is sought over one or more portions of the curve via successive shifts. This method makes it possible to take account of prior knowledge. It is this one which is commonly employed in geophysics for the depthwise or timewise adjusting of seismic horizons or for the correlating of recordings performed in a well and of seismic recordings.
The main drawback of such a method lies in the difficulty in comparing signals of possibly very different shapes, for example if their frequency content is different.
A process for analysing a signal, termed the wavelet analysis process, is known which makes it possible to decompose the said signal as a sum of elementary wavelet functions xcexa8a,b, which each vibrate as sinusoids over a range whose position on an axis is linked to the parameter b and whose width is linked to the parameter a (central frequency), and which are very strongly damped outside this range. The decomposition of a signal with the aid of a family of these wavelets constitutes what is referred to as a xe2x80x9ctime/frequencyxe2x80x9d analysis, since the first and most common decompositions were performed on recordings of the variations of a first quantity as a function of time (the second quantity). In this case, the dimension of the parameter b is that of a time and the dimension of the parameter a is the dimension of the inverse of a time, hence of a temporal frequency.
For further information regarding wavelet decomposition or xe2x80x9ctime/frequencyxe2x80x9d analyses, reference may be made to the article xe2x80x9cL""analyse par ondelettexe2x80x9d [Wavelet analysis] by Yves MEYER et al., published in xe2x80x9cPour la Sciencexe2x80x9d of September 1987, to the work xe2x80x9cWaveletsxe2x80x9d by J. N. COMBES et al. published by Springer-Veriag, or else to the international patent application published under No. WO 92/18941, which documents are incorporated into the present application.
Several types of functions may be used, making it possible to define numerous families of wavelets having different properties. The latter may for example be gaussian, boxcar or triangular functions, real or complex functions, which may or may not be mutually orthogonal. Reference will be made to the above-cited article to ascertain the constraints applicable to these various functions and to others in order to generate wavelet families.
For a specified family of wavelets xcexa8a,b, the xe2x80x9cwavelet transformxe2x80x9d in two dimensions z and x, which is associated with a recording s(z) along the z axis, is defined as the sequence of coefficients Ca,b which each correspond to the integral of the product of the recording s(z) to be analysed times the elementary analysis wavelet xcexa8a,b according to the values of b along the z axis and the values of a along an x axis. In the case where complex wavelets have been chosen to perform the time/frequency analysis of a recording or of a signal, it becomes possible to define the real part, the imaginary part, the modulus or else the phase of the wavelet transform. The coefficients Ca,b are calculated through the well known formula:
Ca,b=∫xe2x88x92oo+ooS(z)a,b(z)dz
Methods and devices for identifying geological structures using wavelet transforms are described in particular in patents U.S. Pat. No. 5,673,191, U.S. Pat. No. 5,740,036 and U.S. Pat. No. 5,757,309 and in the article entitled xe2x80x9cDetection of non stationarites in geological time series: wavelet transform of chaotic and cyclic sequencesxe2x80x9d, by Andreas PROKOPH et al, published in Computers and Geosciences, Vol. 22, Nxc2x0 10, pages 1097-1108, 1996.
However, these latter documents relate either to magnetic and gravitational measurements for distinguishing between relatively deep geological structures and shallow structures, or to means for simulating the succession of structures.
The present invention relates to a method of detecting breaks in logging signals, which uses a wavelet analysis of the said signals.
It is known that the analysis of the logging signals obtained with the aid of well known devices makes it possible to determine the mineralogy, the texture, the type of porous lattice and the fluid content of the formations through which boreholes are drilled. The depthwise alterations in the signals reflect the alterations in the properties of the formations and make it possible to chart their structural and diagenetic sedimentary history.
Within the logging signals it is possible to distinguish breaks which correspond to significant modifications of the nature of the formations which occur over a small depth interval.
Electrofaciological beds may be characterized on the basic of the breaks plotted on at least one of the channels of the logging signal. Inside a bed, each channel of the logging signal shows a continuous variation, on a given depth resolution scale. The noteworthy breaks are used by the geologist for lithostratigraphic correlation purposes. In certain cases, chronostratigraphic correlations are possible by performing an interpretation on the basis of a conceptual model of the alterations of the sedimentary deposits.
Specialists performing the analysis of the logging signals use the noteworthy breaks, in the first step of the interpretation, for the depthwise readjustment of the various signals recorded by the sensors of the logging device which are not all located in front of the same formation at the same time. On either side of the breaks, the logging signal suffers from a shoulder effect over an interval which depends on the resolution of the logging devices and on the contrast of the characteristic logging responses of the formations. This shoulder effect is a source of errors and uncertainty in the interpretations.
The present-day processes for interpreting logging signals are based on processing each sample of the logging signal independently of the samples lying above and below the processed sample, the concept of depth not being involved. Accordingly, the information carried by the alterations of the signal with depth is not taken into account. In order for this information to be taken into account, it is necessary to define breaks over the logging signal and alterations inside the breaks.
The determination of breaks is currently performed manually and requires an experienced operator. The result is both subjective and difficult to reproduce identically. However, these breaks which correspond to the limits of beds or of formations are necessary for depthwise readjustment.
Depthwise readjustment is a fundamental step in all interpretation of logs, since it consists in resetting to the same depth measurements performed by the various sensors of the logging devices, which do not pass simultaneously in front of the same point of the well.
Two types of readjustments are distinguished:
xe2x80x9cintra runxe2x80x9d readjustments, which relate to measurements recorded during the same ascent of a set of mechanically interlinked sensors;
xe2x80x9cbetween runsxe2x80x9d readjustments, which are facilitated by always recording a common log in the various runs, this common log generally being the xe2x80x9cgamma rayxe2x80x9d log which serves as depth reference.
A first readjustment is performed at the time of acquisition and relates only to the measurements performed during the same recording. It is satisfactory only in the best cases and always has to be checked.
There are in existence stations for analysing logs and with the aid of which it is possible to make readjustments. However, the readjustment operations remain manual or, when they are automatic, they relate only to logs of the same kind, the analysis stations being unable automatically to analyse logs of different kinds. Therefore, only readjustments between runs are possible. Moreover, the current processes, based on correlations, do not make it possible to identify, hierarchize and assign a quality index to the correlations.
The aim of the present invention is to propose a method which makes it possible automatically to detect breaks in logging signals or logs and which is able to be applied in respect of depthwise readjustment of the logs recorded.
The subject of the present invention is a method of detecting breaks in logging signals relating to a region of a medium and consisting of logs of different kinds recorded for the said region as a function of depth, of the type consisting in:
selecting a portion from each of the said logs in such a way that all the selected portions have a same depth interval in common, one of the selected portions being regarded as reference portion,
determining a sequence of spatial analysis frequencies,
selecting a parent wavelet function and constructing, from the said parent function, a family of wavelet analysis functions dependent on spatial frequency (or wavenumber) and on depth,
calculating a wavelet transform of the selected portion of each log and for each analysis frequency,
choosing a characteristic quantity of the wavelet transform and in using this quantity as a representation of the wavelet transform, the said method being characterized in that it furthermore consists in:
calculating, for each portion of log selected and for each depth datum, the absolute value of the mean gradient of the characteristic quantity of the wavelet transform for the various analysis frequencies,
selecting, for each portion of log processed, the peaks of the absolute value of the mean gradient of the characteristic quantity, each peak corresponding to a break,
determining the corresponding breaks over the reference log portion,
defining an analysis window centred on each break of the reference log portion, and
selecting the breaks of the other log portions which lie in the analysis window.
An advantage of the present invention lies in the fact that all the curves representative of the various logs recorded are taken into account and processed rapidly (simultaneously or sequentially one after another).
Moreover, the method according to the invention makes it possible to circumvent the shoulder effects linked with the resolution (effectiveness) of the logging devices so as to chop the intervals supplying the logs into beds and to be able to analyse the vertical alterations in their various geological characteristics.
According to another characteristic, the result of the wavelet transform is a complex number and the characteristic quantity of the wavelet transform is the real part of the said complex number. The parent function may for example be a function of the type f(z)=(1xe2x88x92z2)exp (xe2x88x92z2/2).
According to another characteristic, the absolute value of the mean gradient is normalized, the peaks of the absolute value of the mean gradient which are selected are greater than or equal to a predetermined threshold. In particular, the absolute value of the mean gradient is normalized and the threshold for selecting the peaks is equal to or greater than 0.2.
According to another characteristic, the log supplying the reference portion is obtained by gamma ray logging, the said (gamma ray) log being an excellent depth reference since it can be recorded in all types of drilling mud and even through a casing.
According to another characteristic, each processed portion of log is included within an interval of study containing a predetermined number of samples N. In particular, when the number of samples to be processed in a log portion is either less than or greater than the number of samples N of the interval of study, the log is either centred in the said interval and the empty parts of the latter are filled with samples having a value equal to the mean value of the log, or else it is divided into at least two parts each comprising a number of samples less than N, in such a way as to process each part as indicated above.
According to another characteristic, the succession of the spatial analysis frequencies used for the calculation of the wavelet transform has as limits a frequency corresponding to a wavelength of 4 m and a frequency corresponding to a wavelength of 200 m. The succession of the said frequencies is for example a geometric progression. Preferably, ten spatial frequencies are selected, the limits of which correspond to wavelengths of 10 m and 100 m.
Each spatial frequency is analysed independently of the others, without successive filtering. Moreover, choosing the frequencies makes it possible to have a number of wavelet coefficients which is sufficient to carry out a study of their spatial organization, in the depth/frequency plane. In this way, three-dimensional information is obtained linking the depth, the frequencies present in the starting logging signal and the amplitude of the transform.
Thus, the method according to the invention makes it possible to study, for each depth datum, the logging signal at various scales, that is to say over depth intervals whose size differs.
The method according to the invention makes it possible to hierarchize the breaks according to various logging criteria and to give priorities (or quality criteria) in the references which are used in particular in the depth readjustment. Thus, it is possible automatically to process both an xe2x80x9cintra runxe2x80x9d readjustment and a xe2x80x9cbetween runsxe2x80x9d readjustment.